Like if I put my resume on a site, someone has to bid to contact me? Perhaps as an applicant, you can set a base price and a frequency of contact. Maybe you only allow one recruiter to contact you per week or day. If you want to be that recruiter, it'll cost you minimum $1. If more than one recruiter wants to contact you, they bid up the price.
Applicants could regulate the minimum price based on their current status. If they are employed happily, the price is $1000. If they are unemployed, perhaps it's zero with unlimited contacts until they get flooded and then the price goes up.
The economics of such an idea is interesting. It assumes a shift in power from the employer to the applicant. The best of the best will rise to the top and a natural ranking of applicants will evolve based on the bid. Great applicants could sustain themselves on employer interest for a while until recruiters give up trying to gain their interest.
Could something like this work? I suppose it depends on supply and demand of both applicants and jobs.